Differential calc

[XfireZ51]

OK guys. I'd like you to check my math. I am considering changing rear gearing due to the fact that my Z06 wheels are about 1" taller than stock and that my current speedo gear appears to have been there due to the car previously having 4.10s. It now has 3.45s. Using GPS, I find that the speedo to actual error is 10mph at 64 indicated/74 actual. This tells me that my error is ~15.6% tires and everything included. So it seems that the 3.45s are performing actually as 2.91s. If I want to get the performance of 3.45s, I calculate that:

If 3.45 = X*.844 (or 1-.156), then X = 3.45/.844 = 4.0876

Therefore, I need 4.10s in order for the speedo to be correct and for the acceleration to be what it would be with stock gears.

Guess what I'm looking for now?

[Paul Workman]

Originally Posted by XfireZ51

OK guys. I'd like you to check my math. I am considering changing rear gearing due to the fact that my Z06 wheels are about 1" taller than stock and that my current speedo gear appears to have been there due to the car previously having 4.10s. It now has 3.45s. Using GPS, I find that the speedo to actual error is 10mph at 64 indicated/74 actual. This tells me that my error is ~15.6% tires and everything included. So it seems that the 3.45s are performing actually as 2.91s. If I want to get the performance of 3.45s, I calculate that:

If 3.45 = X*.844 (or 1-.156), then X = 3.45/.844 = 4.0876

Therefore, I need 4.10s in order for the speedo to be correct and for the acceleration to be what it would be with stock gears.

Guess what I'm looking for now?

Simple proportion, if I'm not mistaken...

64/74 : 3.45/ X

Solving for "X"

X = 74 x 3.45/64
X = 3.989

Checking:

3.45 is to 3.989 as 64 is to 74

3.45/3.989 = 64/74

Confirmed...the new ratio is 3.989

Or so it seems to me...

P.

[XfireZ51]

Paul,

I think the diff here is that I am looking for a gear that will perform LIKE a 3.45 given the current error I have. I am calc'ing the error as actual/indicated which gives me 15.6%. You're calc'ing the error as indicated v actual which is 13.6%.
The error is 10mph at an indicated 64 or 15.6%.
Your proof works because you substituted the answer for X.

[Gunny]

I created an Excel file that calculates gear ratios ... it should provide the calculations you need.

Click HERE to download. When you open this link you should see a file "GearRatio.xls ... click to download the file. Please note that this link expires in 5 days and is limited to 20 downloads. If you have difficulty with the download please IM me with your email address and I'll send it to you.

George Jones

[Paul Workman]

Originally Posted by XfireZ51

Paul,

I think the diff here is that I am looking for a gear that will perform LIKE a 3.45 given the current error I have. I am calc'ing the error as actual/indicated which gives me 15.6%. You're calc'ing the error as indicated v actual which is 13.6%.
The error is 10mph at an indicated 64 or 15.6%.
Your proof works because you substituted the answer for X.

The ratios beteen speed difference an gear ratios has to be preserved.

Yours (.844) is the result of a common error (when using percentages) stemming from the corruption of the root ratios by first conveting them to percentages and then mulitplying by their antithesis. Apples to oranges in a logical, albeit erroneous manner.

For example, 74/64 = 1.156 or 74 is = 115.6% of 64.

Checking: Let's stick with the ratios... Dividing 74 by 1.156x = 64 = check.

Second check: Inversely, 74 x 1/1.156x = 64. We're good.

But here's the thread of a common mistake: When converting ratios to %, one first multiplies by 100, and then to derive the result as an increase (in this case) we subtract 100 to isolate the change. the antithesis of 15.6% is (in this case) 100% - 15.6% or 84.4%. BUT the reciprical (100%/84.4%) is 118.463% NOT 115.6% which was the orginal ratio 100 x 74/64 or 115.6%

So, keeping with ratio (inv) proportions, the ratio (proportionally speaking) between 64 and 74 is the same ratio that exists between the current 3.45 gear and that of the new gear ratio required to equate to the same ratio in order to get the speedo to agree with the acutal.

Don't feel bad. Retailers make the same mistake all the time by accident (or intentionally). Mark a $100 product up 20% to $120, and then have a 20% reduced price sale; 100%-20% is 80%, but 80% of $120 IS NOT $100! See where this is going?

Keep the ratios intact, and all is well. I'm just sayin.

P.

PS

3 guys check into a cheap hotel room. The clerk initially charges them $30 or $10 each for the room. Later he discovers the room rate was supposed to be $25. The clerk returns to the room with 5 $1 bills. Explaining the error, the guys decide to each take a dollar and leave $2 with the clerk for being so honest. So, in effect, each pays $9 for the room or 3x $9=$27. The clerk keeps $2 and $27 + $2 is $29 NOT $30!!...Where is the missing $1????

Not exactly the same thing, but then sorta IS.

[WVZR-1]

I did this a bit differently but the numbers came closer to PW's. I believe pure math makes PW's correct. The displayed error is .86486xxxxx rounded to .865 so I'd guess if we wanted to correct this at the rear gear we'd need 3.45 x 1.135 or a 3.915xxx. Granted this number required rounding up of the error which resulted in a lower value for the multiplier which makes a result that differs from the 3.989 of PW's.

To get your displayed 64 to the actual 74 requires an equal adjustment?

You could do the 4.10's and correct the speedo error after the install.

With no drive/driven speedo adjustments a 1" plus tire from the 315/35 (25.68) would result in an actual 77 MPH with a 74 displayed I believe.

Wasn't this discussed awhile ago?

[XfireZ51]

Given the display error of 10mph with a display of 64, we know the display error is 15.6%. In order for the display error to be 15.6%, my 3.45 gears are effectively 3.45 x .844 = 2.91

Setting up a proportion,
I can say that
2.91:3.45::3.45:X with X being the new gear
Solving for X
3.45x3.45=2.91X
11.90=2.91X
4.09=X

[ZRapid-1]

OP…… not all your info adds up.

Here’s some scenarios:
1. If you want the same acceleration as you had prior to the Z06 wheel changeover:

• Assuming a stock tire diameter of 25.7 inches and then a changeover to Z06 tire diameter of 26.7 inches
• This is only a change of [(26.7 – 25.7) / 25.7 ] x 100% = 3.89 %.
• Note that this does not correlate to the percentage difference between your speedometer and GPS.
• Assuming you have a 3.45 differential ratio, then a change to 3.45 x 1.0389 = 3.58 will provide equivalent acceleration.
• This change, by itself, will still result in an incorrect speedometer reading.
• This analysis shows that the error is not due to just the Z06 tire changeover. If you put the original 25.7 inch diameter tires back on, you will still see a difference between the speedometer and GPS.

2. If you want the speedometer to match the GPS:

• 64 MPH [Indicated Speed] x TBD = 74 MPH [GPS Actual Speed]
• TBD = 1.156
• Need to increase tire rotation by 15.6%
• 3.45 x 1.156 = 3.989
• A differential ratio of 3.989 (and Z06 tires) will provide the correct speedometer reading. It will also provide greater acceleration than the 3.45 gears and 25.7 inch diameter tire combination.

Here’s my theory,

The car started with 3.45 gears and had the correct matching transmission gear for the speedometer.
The car then was converted to 4.10 gears and matching transmission gear (for 4.10).
Another conversion changed the 4.10 gears back to 3.45 – but left the transmission speedometer gear at 4.10.
You then added larger diameter Z06 tires.
3.989 differential gears and Z06 tires will provide the correct speedometer reading.
25.7 inch diameter tires and 4.10 differential gears will also provide the correct speedometer reading.

Your other choice is to change the transmission speedometer gear if you just want to get a correct speedometer reading.

[WVZR-1]

I guess the difference of opinions here is the calculation of the "hypothetical" gear!

64/74 = .86486..... error

64 X 1.156 = 73.984 for correction

3.45 X .86486 = 2.98 (hypothetical for correction)

2.98 X 1.156 = 3.448 for present ratio

3.45 X 1.156 = 3.98 required for speedo correction

I originally approximated some things and the adjustment I used to correct was in error. See what you think of this rationale!

[Paul Workman]

Originally Posted by XfireZ51

Given the display error of 10mph with a display of 64, we know the display error is 15.6%. In order for the display error to be 15.6%, my 3.45 gears are effectively 3.45 x .844 = 2.91

Setting up a proportion,
I can say that
2.91:3.45::3.45:X with X being the new gear
Solving for X
3.45x3.45=2.91X
11.90=2.91X
4.09=X

Dom... As other too have pointed out, your error is rooted in the .844 number

The ratios between speeds has to equal the ratio between gear changes, yes?

64:74::3.45:3.989 are valid.

74/64 = 1.156 and the recip. is 1/1.156 = .856, NOT .844.

You can proove it yourself: try applying .844 or 1/.844 to either the 64 or the 74 and see if the other is derived...NEITHER WILL. 74 X .844 = 62.45, NOT 64. 64 X 1/.844 = 75.829 NOT 74

An engineering friend of mine used to call it the "Bugger Factor". That's where a calcuation starts with an answer in imbedded in the mind, and if by chance the treatment delivers a number close to the expected answer, the "Bugger Factor" takes over the mind and the assumption is made. (It is dangerous to assumes a single calc is correct. Hence, PROOFs are necessary to verify the root numbers can be reproduced. Such is not the case here as WVZR-1 and ZeeAreOne also demonstrated.)

The "Bugger Factor" in the soup is the result of you calc being 4.09 and is so close to the expected 4:10 that the calc must be valid...But, it is flawed.

I say we're splitting hairs, in reality:

I suggest you install a 4.09 or 4.10 gear to get back to the equiv of the stock 3.45*, because, 1)that ratio shouldn't be hard to find, whereas the 3.99??? 2) The Bugger Factor will be satisfied because your error will only be about 2.5%, or approx 1.2 mph at 50 mph indicated - well within the window of acceptable error for a spedo, and 3) your shift light is all that really matters on the strip.

*Or going with a 4.56 would put you pretty close to the same as going from a 3.45 to a 4.09 on stock wheels/tires...Just a thought.

And, as the saying goes...your mileage may vary! (Just don't take a job at JPL. They're calculating the trip to Mars right now, and wouldn't want to land on one of its moons instead!)


P.